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I need to solve a large-scale generalized network flow problem.

For reference, it is a pure network-flow model with the exception that arcs have a positive coefficient applied to flow on them. In my case I have supply nodes from which I send flow to sink nodes that absorb them. The flow, however, incurs a loss depending on the distance between the two nodes.

Google OR-Tools has an excellent network-flow solver, but only for pure flow models. Is there a publicly available and reasonably mature solver for generalized network models? If not, could anyone recommend an easy-to-implement solution algorithm that I can implement myself quickly?

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    $\begingroup$ Have you tried solving it as an LP? $\endgroup$
    – RobPratt
    Commented Nov 13, 2021 at 21:01
  • $\begingroup$ I did not yet, but it is the first thing I will try next week. I prefer originating flows to be integer, but probably can live with fractional values. I am kind of spoiled with the speed of Google's network flow solver, so hoping to find something like that for the generalized version. Also, I may have to solve this problem many times so computational requirement may be an issue. $\endgroup$ Commented Nov 13, 2021 at 21:05
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    $\begingroup$ Unlike pure network flow, generalized network flow will not typically yield integer optimal solutions. $\endgroup$
    – RobPratt
    Commented Nov 13, 2021 at 21:10
  • $\begingroup$ Good point, did not think of that. Given that commercial LP solvers are very fast these days, it should do it for me. Still I am curious about the availability of generalized network flow solvers. For very large problems it could make a significant difference compared to an LP solver. $\endgroup$ Commented Nov 13, 2021 at 21:14
  • $\begingroup$ What is the theoretical or computational evidence that there is a specialized algorithm for generalized network flows that will beat a general LP optimizer? Is there any collection of benchmark instances of generalized network problems? $\endgroup$ Commented Nov 15, 2021 at 7:45

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